We tentatively investigate the root-mean-square (rms) nuclear charge radii of odd-A Po and Pb isotopes plus Tl isotopes, particularly concerning these difficultly-detected nuclei along with short lifetimes, via various data on a decay. Within the density-dependent cluster model, the density distributions of studied daughter nuclei are determined by exactly reproducing the corresponding experimental a decay half-lives, which leads the final results of nuclear charge radii. In addition, our recently proposed formula deducing the charge radii is extended to this study for comparison. Whether it concerns the ground or isomeric state of target nuclei, the extracted nuclear charge radii are found to be in good agreement with the measured values. Sequential predictions on the rms charge radii are subsequently made for these neutron-deficient nuclei and especially for the rarely detected Bi isotopic chain, which are expected to be useful for future measurements. Moreover, the variety of a-preformation factors is analyzed in the scheme of valence nucleon number to pursue the further improvement of the model. This may be considered as an effective effort to obtain the charge radii of ground and even low-lying excited states for exotic nuclei near the proton-dripline. (C) 2015 Elsevier B.V. All rights reserved.